Abstract
We formulate a mathematical model of a rolling “molecular wheelbarrow”—a two-wheeled nanoscale molecular machine—informed by experiments on molecular machines recently synthesized in labs. The model is a nonholonomic system (briefly, a system with non-integrable velocity constraints), for which no general quantization procedure exists. Nonetheless, we successfully embed the system in a Hamiltonian one and then quantize the result using geometric quantization and other tools; we extract from the result the quantum mechanics of the molecular wheelbarrow, and derive explicit formulae for the quantized energy spectrum. We also study a few variants of our model, some of which ignore the model’s nonholonomic constraints. We show that these variants have different quantum energy spectra, indicating that in such systems one should not ignore the nonholonomic constraints, since they alter in a non-trivial way the energy spectrum of the molecule.
Highlights
The awarding of the 2016 Nobel Prize in Chemistry for the “design and synthesis of molecular machines” is evidence of the immense interest in—and importance of—molecular machines
In5 researchers reported “rolling a double-wheel molecule on an Au(111) surface over a short path”. In another example[6], a four-“paddle-wheeled” nanocar was synthesized and reported to roll in a fairly linear manner upon a metallic surface; each 360-degree wheel rotation was achieved via a series of alternating electronic and vibrational excitations. These examples of rolling nanovehicles are intriguing because while the mechanics of rolling are well-understood at the macroscopic scale—this is the subject of nonholonomic mechanics—there is no known theory of rolling at the nanoscale
We chose the boron-subphthalocyanine double-wheel molecule synthesized in[9] and manipulated in[5] by the tip of an scanning tunneling microscope (STM) on a gold surface to develop our mathematical model of the molecular wheelbarrow
Summary
The awarding of the 2016 Nobel Prize in Chemistry for the “design and synthesis of molecular machines” is evidence of the immense interest in—and importance of—molecular machines (single molecules consisting of functional components). In5 researchers reported “rolling a double-wheel molecule on an Au(111) surface over a short path” In another example[6], a four-“paddle-wheeled” nanocar was synthesized and reported to roll in a fairly linear manner upon a metallic surface; each 360-degree wheel rotation was achieved via a series of alternating electronic and vibrational excitations. These examples of rolling nanovehicles are intriguing because while the mechanics of rolling are well-understood at the macroscopic scale—this is the subject of nonholonomic mechanics—there is no known theory of rolling at the nanoscale (i.e., no “quantum nonholonomic mechanics”). This latter point has important ramifications for anyone working with nanomachines and measuring their spectroscopic properties, since it suggests that one should not ignore a rolling nanovehicle’s nonholonomic constraints in the course of analyzing the quantum mechanics of the system
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
